Calibration Requirements Document SPIRE

SUBJECT: Calibration Requirements Document

PREPARED BY: Bruce Swinyard

DOCUMENT No: SPIRE-RAL-PRJ-001064

ISSUE: DRAFT for Comment Date: 3 January 2002

CHECKED BY: Matt Griffin Date:

APPROVED BY: Walter Gear

Jean-Paul Baluteau

Date:

Distribution

Matt Griffin Principal Investigator (Cardiff University)

Laurent Vigroux Co-Principal Investigator (CEA)

Walter Gear Project Scientist (Cardiff University)

Jean-Paul Baluteau Project Scientist (LAM)

Ken King Project Manager (RAL)

Bruce Swinyard Instrument Scientist (RAL)

Jamie Bock Co-I (JPL/Caltech)

Jason Glenn Assoc. Scientist (University of Colorado)

Peter Hargrave Cal Source Scientist (Cardiff University)

Gary Davis Co-I (USK)

David Smith AIV Manager (RAL)

Gustav Ollofsson Co-I (Stockholm)

Poalo Saraceno Co-I (IFSI)

Sergio Molinari Assoc. Scientist (IFSI)

Gillian Wright Co-I (ATC)

Sunil Sidher ICC (RAL)

Tanya Lim ICC (RAL)

Matt Fox ICC (IC)

Seb Oliver ICC (Sussex University)

Marc Sauvage ICC (CEA)

Christophe Morriset ICC (LAM)

Ch C ha an ng ge e R Re e c c o o rd r d

ISSUE DATE

Draft for comment 3 January 2002 First reasonable version sent out for comment to interested

parties

Table of Contents

1. Scope...8

2. Derivation of the Calibration Requirements...8

2.1 Scientific Requirements...8

2.2 Additional Scientific Requirements ...13

3. Baseline Calibration and Performance Verification Requirements ...15

3.1 Ground Calibration ...15

3.1.1 Basic test facility ...15

3.1.2 SRD-R1/SRD-R2 Ultimate sensitivity in photometer mode ...15

3.1.3 SRD-R1/SRD-R2/SRD-R5/SRD-R15 Measurement of the Spatial Impulse Response Function and Instrument Throughput...20

3.1.4 SRD-R6/SRD-R8 Position of the Pixels on the Sky...24

3.1.5 SRD-R8/SRD-13/SRD-14 Crosstalk Map; Detector Frequency Response and Linearity ...26

3.1.6 SRD-R10/CRD-SR1 Spatial Relative Responsivity and Pixel NEP Map...29

3.1.7 CRD-SR2/CRD-SR3/CRD-SR4 Relative Spectral Responsivity; Channel Central Wavelength and Bandpass; Out of Band Rejection ...30

3.1.8 SRD-R13 Temporal Relative Responsivity ...32

3.1.9 SRD-R12 Photometer Absolute Radiometric Accuracy ...34

3.1.10 CRD-SR5 Rejection of Radiation from Outside the Field of View...35

3.1.11 SRD-R17 FTS Sensitivity – determination of Zero Path Difference Position...36

3.1.12 SRD-R17/SRD-R20/SRD-R22 Velocity Stability; Minimum and Maximum Achievable Resolution ...37

3.1.13 SRD-R21 Spectrometer Spectral Response Function ...40

3.1.14 SRD-R19 Spectrometer Absolute Radiometric Accuracy...41

3.2 In orbit calibration ...42

3.3 AOT Verification...44

4. Ground calibration facility outline requirements...45

Glossary

ADC Analogue to Digital Converter

AIV Assembly, Integration and Verification AME Absolute Measurement Error

AME Absolute Measurement Error AOCS Attitude and Orbit Control System APART

APE Absolute Pointing Error

ASAP Advanced Systems Analysis Program

AVM Avionics Model

BDA Bolometer Detector Array

BFL Back Focal Length

BRO Breault Research Organization BSM Beam Steering Mirror

CDMS Command and Data Management System CDMU Command and Data Management Unit CDR Critical Design Review

CMOS Complimentary Metal Oxide Silicon CPU Central Processing Unit

CVV Cryostat Vacuum Vessel DAQ Data Acquisition

DCU Detector Control Unit = HSDCU DPU Digital Processing Unit = HSDPU DQE Detective Quantum Efficiency EGSE Electronic Ground Support Equipment EGSE Electrical Ground Support Equipment EMC Electro-magnetic Compatibility EMI Electro-magnetic Interference

ESA European Space Agency

FCU FCU Control Unit = HSFCU

FIR Far Infrared

FIRST Far Infra-Red and Submillimetre Telescope

FOV Field of View

F-P Fabry-Perot

FPU Focal Plane Unit

FTS Fourier Transform Spectrometer FWHM Full Width Half maximum GSFC Goddard Space Flight Center

HK House Keeping

HOB Herschel Optical Bench

HPDU Herschel Power Distribution Unit HSDCU Herschel-SPIRE Detector Control Unit HSDPU Herschel-SPIRE Digital Processing Unit HSFCU Herschel-SPIRE FPU Control Unit HSO Herschel Space Observatory

IF Interface

IID-A Instrument Interface Document - Part A

IID-B Instrument Interface Document - Part B IMF Initial Mass Function

IR Infrared

IRD Instrument Requirements Document IRTS Infrared Telescope in Space

ISM Interstellar Medium

JFET Junction Field Effect Transistor LCL Latching Current Limiter LIA Lock-In Amplifier

LVDT Linear Variable Differential Transformer MAC Multi Axis Controller

MCU Mechanism Control Unit = HSMCU MDM

M-P Martin-Puplett

NEP Noise Equivalent Power NTD Neutron Transmutation Doped

OBS On-Board Software

OMD Observing Modes Document OPD Optical Path Difference

PACS Photodetector Array Camera and Spectrometer PCAL Photometer Calibration source

PLW Photometer, Long Wavelength PMW Photometer, Medium Wavelength POF Photometer Observatory Function PROM Programmable Read Only Memory PSW Photometer, Short Wavelength PUS Packet Utilisation Standard SCAL Spectrometer Calibration Source

SCUBA Submillimetre Common User Bolometer Array SED Spectral Energy Distribution

SMEC Spectrometer Mechanics SMPS Switch Mode Power Supply

SOF Spectrometer Observatory Function

SPIRE Spectral and Photometric Imaging Receiver SRAM Static Random Access Memory

SSSD SubSystem Specification Document STP Standard Temperature and Pressure

SVM Service Module

TBC To Be Confirmed

TBD To Be Determined

TC Telecommand

URD User Requirements Document

UV Ultra Violet

WE Warm Electronics

References Applicable Documents

AD1 SPIRE Scientific Requirements SPIRE-UCF-PRJ-000064

AD2 SPIRE Instrument Qualification Requirements SPIRE-RAL-PRJ-000592

Reference Documents

RD1 SPIRE Design Description Document

RD2 “Long Wave Optics”, Derek Martin and John Bowen, IEEE Trans . Microwave Theory

and Techniques 41 Oct 1993, pp1676-1690

1. S COPE

In this document the calibration requirements for the Herschel SPIRE instrument for both ground and in- orbit testing are laid out. This document will evolve during the instrument definition and subsequent phases as the instrument operation and performance is better understood. It will also be updated in line with the Herschel calibration requirements as and when they are established.

2. D ERIVATION OF THE C ALIBRATION R EQUIREMENTS

The primary scientific aim of the Herschel SPIRE instrument is to provide high accuracy three band photometry of point like objects for deep surveys in the 200 to 670

m band. A secondary scientific programme is the medium resolution spectroscopy and low resolution spectrophotometery of point sources. To these ends the instrument has been designed with two channels (RD1):

- A three band photometer with three fixed pass bands and three arrays employing single mode feedhorns to couple the radiation from the Herchel telescope and SPIRE optics onto NTD Ge bolometer detectors – this is referred to as the photometer throughout this document.

- A two band Fourier Transform Spectrometer using the amplitude beam splitters and the same detectors technology as the photometer – this is referred to as the spectrometer throughout this document.

The Science Requirements Document (AD1 hereafter referred to as the SRD) sets out the top level performance and calibration requirements that the instrument must meet in order that it will fulfil the scientific programme of the Herschel mission.

In this section we take each of the scientific requirements and indicate those which require some aspect of the instrument performance to be measured or characterised in order to verify that the scientific requirement is met. The starting point for this is AD1 and these are discussed in section 2.1. However, some additional top-level requirements are needed in order to verify compliance with those in AD1 – these are described in section 2.2.

2.1 Scientific Requirements

The scientific requirements in the SRD can be broken down into two main categories: those that only

drive the basic design of the instrument and those that specify the accuracy to which the instrument

performance must be characterised. There is of course some blurring between the two but here we

wish to distinguish those that will determine what calibration measurements need to be carried out and to

what accuracy. In table 1 the scientific requirements are repeated from the SRD in short form and

comment made on whether they require calibration measurements to be made.

SRD- ID

Requirement Comment Instrument

level calibration?

SRD- R1

The photometer shall be capable of a 60 sq. deg extragalactic survey to 1-σ limit of 3 mJy in all bands in 6 months or less

This defines the basic

performance requirements for the instrument. All aspects of the instrument performance must be compatible with this requirement

Yes

SRD- R2

The photometer shall be capable of a 1sq. deg galactic survey to a 1- σ limit of 3mJy at 250 µ m in 1 month or less

The basic performance

requirement here is easily met if SRD-R1 is satisfied with the exception perhaps of the ability to observe a crowded field of bright point and extended sources.

Yes

SRD- R3

Maximising the “mapping speed” at which the confusion limit is reached…. Is the primary science driver.

This is a statement about the priority of the quality of the PSF over the size of the FOV of the instrument and was used to drive the design

No

SRD- R4

The photometer observing modes should provide a mechanism for telemetering undifferenced samples to the ground

This is a statement about the problems of source identification from chopped observations and was used to define the instrument design.

No

SRD- R5

The photometer shall have an observing mode the permits accurate measurement of the point spread function.

The qualifying text associated with this requirement states that the psf shall be measured “to very high accuracy”. This requirement is therefore associated both with the design of the instrument and the calibration of the main beam of the instrument. Some qualification of “very high” is required

however!

Yes

SRD- R6

Optical field distortion<10% This is set out as a design

requirement. The requirement on the accuracy of the actual positions of the pixels is not explicitly detailed, although some limit is set by SRD-R15. We will interpret this as a requirement to map the pixel positions as a calibration measurement.

Yes

SRD- R7

Photometer FOV at least 4x4 arcminutes

A design driver only No

SRD- ID

Requirement Comment Instrument

level calibration?

SRD- R8

Crosstalk <1% (0.5% goal) for adjacent detectors and 0.1%

(0.05% goal) non nearest neighbours.

A complex requirement involving everything from the optical input to the multiplexing and the ADC!

An end-to-end calibration is required to produce a cross talk map.

Yes

SRD- R9

Maximum chop throw 4 arcmin minimum 10 arcsec

A design requirement for the BSM. No requirement is set on the repeatability or stability of the chopping mirror. These are in fact set as requirements on the BSM and will be dealt with as a sub-system issue – see AD2.

No

SRD- R10

The rms detector NEP variation across any photometer array

<20%

A complex requirement involving everything from the optical input through to the stability and noise of the amplifiers. An end-to-end calibration is required to produce a responsivity and noise map.

Yes

SRD- R11

The photometer dynamic range for astronomical signals shall be 12 bits or higher

Note the use of a number of bits here is incorrect – the dynamic range requirement is 4000. How this is encoded into bits is an implementation issue

This is a design driver for the instrument. The calibration is dealt with under SRD-R14.

No

SRD- R12

SPIRE absolute photometry accuracy shall be 15% or better at all wavelengths with a goal of 10%

Defines the end-to-end calibration accuracy required for both point sources and extended emission.

Both sub-system (filters and detectors) and instrument level calibration will be required to verify this.

Yes

SRD- R13

The relative photometric accuracy should be shall be 10% or better at all

wavelengths, with a goal of 5%

This refers to temporal

repeatability of the measurement of a known source. This will require the characterisation of the temporal stability of the system – especially the thermal stability.

Yes

SRD- ID

Requirement Comment Instrument

level calibration?

SRD- R14

SPIRE photometric

measurements shall be linear to 5% over a dynamic range of 4000 for astronomical signals.

This defines the usable dynamic range of the system and is

assumed to go from the confusion limited sensitivity (let us say a S/N of 20 in a 1 hour observation

~0.02 mJy) to a signal 4000x higher (about 80 Jy on this definition). The instrument photometric calibration shall encompass at least this range of signal inputs.

Yes

SRD- R15

…the overlapping sets of

…detectors…should be co- aligned to within 2 arcsec on the sky (goal 1 arcsec)

This is a design requirement that will need verifying during instrument alignment. The ultimate test will be done using the detectors themselves and a broad band FIR source.

Yes

SRD- R16

Spectrometer optimised for point sources but with an imaging capability…

Design driver – no calibration required

No

SRD- R17

The FTS sensitivity shall be limited only by the photon noise from the telescope

Note this requirement should be changed to include the photon noise from the calibrator – otherwise it is impossible to meet!

This looks superficially like a design driver – however it is a complex matter and actually requires a good deal of calibration to ensure that the requirement is met.

Yes

SRD- R18

The spectrometer dynamic range for astronomical signals shall be 12 bits or higher

Note the use of a number of bits here is incorrect – the dynamic range requirement is 4000. How this is encoded into bits is an implementation issue

This is a design driver for the instrument. There is no linearity requirement for the spectrometer – is it assumed to be the same as for the photometer? Therefore SRD-14 pertains?

No

SRD- ID

Requirement Comment Instrument

level calibration?

SRD- R19

The FTS absolute photometry at the required spectral resolution shall be 15% or better at all wavelengths with a goal of 10%.

Defines the end-to-end calibration accuracy required for both point sources and extended emission.

Both sub-system (filters and detectors) and instrument level calibration will be required to verify this.

Yes

SRD- R20

The FTS shall be capable of making spectrophotometric measurements with a resolution of 2 cm

with a goal of 4 cm

The minimum resolution

achievable is a complex function of a variety of instrument performance factors. An end to end test will be required to

characterise the achievable photon limited minimum resolution (see SRD-17 as well)

Yes

SRD- R21

The width of the FTS instrument response function at the

required resolution shall be uniform to within 10% across the FOV

The line width could be affected by vignetting of the off-axis pixels and increased beam shear at off axis positions. This is both a design driver and needs verification at instrument level.

Yes

SRD- R22

The maximum spectral

resolution of the FTS shall be at least 0.4 cm

with a goal of 0.04 cm

Note that the spectral resolution is defined as the FWHM of the response function assuming linear (triangular) apodisation of the raw interferogram

The maximum resolution is governed both by the physical movement of the SMEC and by any loss in fringe contrast due to beam shear and vignetting. This can only be characterised at instrument level.

Yes

SRD- R23

The SPIRE photometer shall have a an observing mode capable of implementing a 64- point jiggle map…

A design driver – there will be a general requirement to

characterise all SPIRE observing modes but this isn’t a specific driver on the instrument calibration.

No

SRD- R24

The photometer observing modes shall include provision for 5-point or 7 point jiggle maps…

A design driver – there will be a general requirement to

characterise all SPIRE observing modes but this isn’t a specific driver on the instrument calibration.

No

SRD- ID

Requirement Comment Instrument

level calibration?

SRD- R25

The photometer shall have a peak-up mode…

A design driver – there will be a general requirement to

characterise all SPIRE observing modes but this isn’t a specific driver on the instrument calibration.

No

2.2 Additional Scientific Requirements

Some requirements have not been specifically identified in the SRD but will also need calibration. These are given in the table below and are given CRDS-R# identifications as new scientific requirements to be tested during instrument calibration.

ID Requirement Comment Instrument

level calibration?

CRD- SR1

The photometer and spectrometer relative response across an individual array shall be known to within TBC% with respect to any given pixel on the array.

This is the relative calibration between two detectors on a single array. It is extremely important that this is very well established in order to allow co-addition of the signal seen from a source as it is scanned or chopped across the arrays.

Yes

CRD- SR2

The relative response of the spectrometer at any wavelength within the instrument passband shall be known to within TBC%

with respect to the response at any given wavelength.

One of the most important scientific projects for the FTS is the ratio of intensities of lines at different wavelengths. The relative calibration from point to point in the spectral range, including between detector bands, is extremely important.

Yes

CRD- -SR3

The relative response of the photometer as a function of wavelength shall be known to within TBC% with respect to the response at any given wavelength.

The actual response vs

wavelength functions for each of the photometer bands are required for the colour correction of the source intensity. The equivalent width and bandpass centroid can be derived from these functions and are also used for determining the sensitivity of the instrument.

Yes

ID Requirement Comment Instrument level calibration?

CRD- SR4

The spectral out of band rejection of the filtering on the instrument shall be such as to prevent contamination of the survey data by any non-legitimate source emission.

The out of band rejection of the filters will be tested for each individual filter but will not be fully evaluated for the whole optical train except at instrument level. It is important that there are no spectral leaks in the MIR and NIR bands as bright stars etc will otherwise appear as legitimate sources in the surveys.

Yes

CRD- SR5

The instrument shall be designed so as to reduce the straylight from sources outside the field of view of the instrument to less than 5%

of the legitimate background from the Herschel telescope.

This is the instrument part of the straylight budget defined in the IID-A. The control of straylight onto the detectors is done by optical filtering (see CRD-SR4);

the use of “clean” optical stops and baffles and by keeping the instrument itself cold. Some assessment of the instrument’s ability to reject radiation from sources outside the nominal field of view must be made to ensure its compatibility with this

requirement.

3. B ASELINE C ALIBRATION AND P ERFORMANCE V ERIFICATION

R EQUIREMENTS

We can now take those SRD requirements identified as needing calibration or performance verification and break the basic requirement into the parts of the instrument performance that require verification and calibration on the ground and in flight.

This section is in two parts: in the first the calibration requirements are discussed in some more detail and the method of verification and calibration on the ground is detailed. The parameters required for calibration of the instrument data are introduced and given a nomenclature that will be used throughout this and other documentation. In the second section those calibration measurements that will need to be repeated in flight are discussed together with possible methods for carrying them out.

3.1 Ground Calibration

3.1.1 Basic test facility

We can start with the basic assumption that the ground calibration and test facility for the instrument will consist of a cryostat that will allow the instrument to be operated at temperatures and background loadings representative of flight. We can also assume that some form of optical simulator is present that presents the instrument with an optical beam representative of the Herschel telescope. The

requirements on the ground calibration facility are discussed further in section 4.

3.1.2 SRD-R1/SRD-R2 Ultimate sensitivity in photometer mode

The sensitivity of the instrument is characterised by the Noise Equivalent Power (NEP) usually quoted in W Hz

. The NEP is given in terms that will be measured in practice by:

NEP = R

V

δ

<

W Hz

(1)

Where <

V> is the voltage noise on the signal referred to the input of the JFET amplifiers measured in a bandwidth of 1 Hz – equivalent to an integration time of 0.5 seconds – and R is the responsivity of the system measured in V/W, again referred to the input of the JFET amplifiers (i.e. all electronics gains removed). Immediately we have to define at which point in the detection system we define this responsivity, and therefore the NEP. The only measure of astronomical interest is to refer this to the input of the instrument, which can then be referred to the input of the telescope as the Noise Equivalent Flux Density (NEFD) knowing the telescope area and spectral bandwidth of the instrument.

NEFD =

λ

tel∆

instrument

A

NEP W cm

m

Hz

(2)

where A

is the telescope geometric area, if we assume that all coupling efficiencies are factored into the instrument NEP, and

is the equivalent width of the detector bandpass. This NEFD is then the

♦ Conversion to Janskys from W cm^-2 µm^-1 is given by I(Jy) = I(sensible units)*λ²/3e-16

minimum detectable flux per beam in a 0.5 second observation for a source that uniformly fills the field of view of a detector.

In flight the instrument will be background limited by the flux of photons from the telescope, each detector will receive power from the telescope given by:

P

= A

B

(T)

Watts (3)

Here AΩ

is the throughput (also called the etendue or grasp) of the system; εΒ

(T) is the blackbody power emitted by the telescope at temperature T and emissivity

;

is the transmission efficiency of the instrument from the input aperture to the front of the feedhorn and η

the detector quantum

efficiency referred to the front of the feedhorn. The power received at the entrance to the instrument is given by:

P

= AΩ

(T) ∆λ Watts (4)

The NEP referred to the instrument aperture due to the photon shot noise is (ignoring the Bose-Einstein correction)

NEP

= (2P

hc/

)

W Hz

(5) And the total NEP will be given by

NEP

= (NEP

+ NEP

)

W Hz

(6)

Where NEP

is the intrinsic NEP of the detector in the absence of any photon background but measured under the same operating conditions and referred to the input of the instrument.

We can measure the NEP of the detectors with a blanked off instrument – or equivalently with a blanked off detector – this can be referred to the input of the instrument by removing the instrument efficiency:

NEP

=

opt

NEP

η

W Hz

(7)

and, knowing the absolute power falling on the instrument, we can derive NEP

. This can be compared to the direct measurement of the NEP using the measured noise and the responsivity referred to the instrument aperture. This can be derived from the responsivity measured at the detector unit level and knowledge of the instrument efficiency:

R

=

R

V/W (8) Two basic methods of deriving the instrument sensitivity are open to us.

1. If we can measure the responsivity, and therefore the NEP, of the detectors at unit level under

the same operating conditions (temperatures and background loading) and using the same

spectral input, and we can know the efficiency of the instrument from the input aperture to the

feedhorns by modelling or direct independent measurement, then we can derive the instrument responsivity. Measurement of the voltage noise on the DC output of the system with input power somewhere representative of flight then gives us the instrument level NEP directly.

We then need only measure the spectral bandpass to obtain the NEFD.

If we also know the absolute power falling on the instrument aperture (see next point) we can compare the estimated total NEP in equation (6) with that directly measured.

2. If we have an absolutely calibrated blackbody in the beam of the instrument and can measure the instrument throughput and spectral bandpass we can know absolutely the power falling on the instrument aperture. We can derive the responsivity of the instrument by varying the temperature of the blackbody (and therefore the power) and measuring the voltage response of the detectors (using V-I curves for instance). Measurement of the voltage noise on the DC output of the system with the input power set to the in flight level then gives the instrument NEP.

In practice both of these methods are likely to be used and both have their advantages and difficulties.

In particular the independent measurement of the instrument efficiency,

, is problematic. It can be obtained by comparison of the responsivity measured at detector unit level and at instrument level but this is a) non-independent and b) pre-supposes that the measurement conditions were equivalent at unit and instrument level. Alternatively we can measure the characteristics of the component parts of the optical train and combine these into an optical model of the instrument. We should attempt to measure all the relevant parameters (see table below) and cross check the end-to-end derivation against the product of the unit level derived parameters.

The Science Requirement actually refers to the detection of point sources to a 1-

limit. Therefore we are interested in knowing the signal to noise ratio of the background limited performance of the

instrument to the detected flux from a point source. The signal to noise is given by:

σ =

instrument sig

NEP t 2

P

and the signal from a point source with a flux spectrum of S

W cm

um

is given by P

= S

η

η

Watts (11)

Where

is the coupling efficiency between the instrument and the beam pattern from the telescope.

To fulfil the verification of the requirement we therefore need to measure the relative response of the instrument to a point and an extended source or, knowing the illumination pattern of the instrument on the telescope pupil, use optical modelling to calculate

.

It is pertinent to note here that we do not in practice need to know the absolute detector quantum

efficiency η

because we always measure the signal in terms of volts – this is converted to power at

the front of the feedhorn by using the detector responsivity, which already includes the detector quantum

efficiency.

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-1

Detector Absolute Responsivity (R

– V/W)

Responsivity of an individual detector referred to the input to the feedhorn. This is used to cross check the measured instrument responsivity against that predicted from the unit level calibrations.

Measured at unit level using a blackbody placed in the front of the feedhorn and any associated feed optics. Measurement of voltage response vs input power done by V-I curve method with different temperatures of the blackbody.

CRD-PAR-2

Instrument Absolute Responsivity

(R

– V/W)

DC responsivity of each detector referred to the input to the instrument. This is the basic correction between Watts at the entrance of the instrument and volts referred to the input of the warm amplification chain. It is a function of the operating

conditions (temperature; bias;

background loading etc) of the detectors. It must be determined under a range of conditions to create a matrix that will allow us to predict what it will be during flight and to pick the optimum conditions for instrument operation.

Measured at instrument using a blackbody placed in the beam of the instrument beam.

Measurement of voltage

response vs input power done by V-I curve method with different temperatures of the blackbody.

Under each loading the voltage noise is also measured to give the DC NEP as a function of position in the field of view.

All detectors in all arrays can be read out simultaneously thus giving both the absolute responsivity and the relative responsivity of each pixel.

The same measurement can be made with the instrument in different operating conditions.

CRD-PAR-3

Instrument Efficiency

– no units)

End-to-end transmission efficiency of the instrument optical train – allows reference of detected signal to the power received at the input aperture of the instrument

Can be deduced from absolute efficiency measurements over a given waveband of individual components and/or as a single end-to-end efficiency

measurement at instrument level with known input power and detector responsivity.

CRD-PAR-4

Channel Equivalent Bandpass

(∆λ − microns)

The effective spectral width of the end-to-end optics; filters and detectors on each of the three photometer channels – used to convert from detected power to power per unit frequency (wavelength) interval.

Can be deduced from spectral

relative efficiency measurements

of individual components and/or

as a single end-to-end efficiency

measurement at instrument level

– see later.

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-5

Pixel Nominal Load Noise Map

(

V

– Volts)

Measured voltage noise of the detection system for each detector in each array referred to the input of the warm amplifier chain. This is used to verify the measured NEP under nominal background loading. It is a function of the operating conditions (temperature; bias;

background loading etc) of the detectors. It must be determined under a range of conditions to create a matrix that will allow us to predict what it will be during flight and to pick the optimum conditions for instrument operation.

The background into the instrument is controlled either using the shutter or by staring at a black surface of well known temperature that fills the FOV of the instrument. The noise is measured for all detectors in all arrays simultaneously.

The same measurement can be made with the instrument in different operating conditions.

Initially this test will done using a well calibrated external

blackbody; the shutter emission will be calibrated against this blackbody in order to provide the same or similar conditions during system level testing.

CRD-PAR-6

Instrument Throughput (AΩ

steradian)

Etendue or grasp of the instrument which defines how the radiation from an extended source is coupled into the bolometers. It is required to convert from power detected to power per unit area per unit solid angle.

Difficult! In principle (Derek Martin (RD2)) the A and the

can be measured separately by measuring the beam pattern at the pupil and at field. See discussion in section 3.1.3.

CRD-PAR-7

Point Source Coupling Efficiency.

(

– no units)

This is the relative amount of energy from the telescope amplitude pattern that, when the telescope is illuminated by a parallel beam, is detected by the bolometer. It is required to convert from detected power from a point source to actual input power into the instrument.

One method (perhaps the

simplest?) is to compare the

detected signal from an extended

and a point source of the same

emitted power per unit area and

per unit solid angle. This could

be achieved using a variable

aperture in front of a hot

blackbody placed at the input

focal plane of the telescope

simulator. Alternatively this is

also given (in principle) by

measurement of the relative

illumination pattern of the

instrument on the telescope

secondary – see below.

3.1.3 SRD-R1/SRD-R2/SRD-R5/SRD-R15 Measurement of the Spatial Impulse Response Function and Instrument Throughput

The Spatial Impulse Response Function describes the shape of the angular response of an individual pixel in the bolometer arrays to a delta function or point source. The most obvious method of determining the impulse response function is to scan a point source across the field of view of an individual detector at the input focal plane of the telescope simulator. However the interpretation of this measurement will suffer from the need to have, inevitably, a source of finite extent and from any distortion of the field due the systematic behaviour of the telescope simulator. The use of a fully coherent source with a small angular spread and fully coherent phase is desirable as this can be

modelled to a very high degree of fidelity and therefore de-convolution of the source from the measured response is very much easier.

Another way to determine the point spread function is to measure the response of the instrument to a point source scanned across the image of the instrument cold stop as projected outside the instrument.

The Fourier transform of this response then gives the impulse response function of the instrument on the sky. Making the measurement in this fashion has the advantage that a source of reasonably extent can be used as it only has to be small compared with the size of the pupil image and the beams of all detectors can be measured simultaneously. The disadvantage of this method is that no phase information is found and so aberrations in the optics are not detected and the source will need to be carefully designed to avoid problems with straylight.

To measure the throughput of the instrument we need to measure the area of the beam at one of the conjugate planes (focal plane or pupil plane) and the angular extent of the beam at the other. To illustrate how this can be done by measurement of the response of the instrument we can derive the throughput for a single Gaussian mode as follows.

The radius of the waist (defined as the Half Width Half Maximum of the intensity pattern) of a single mode diffraction limited system at the focal plane is given by (Goldsmith):

w

=

λ

) /#

f (

2 mm (12)

where f/# is the focal ratio of the final optics and the wavelength, λ, defines the units (millimetres here by convention). The opening angle of the beam from a single mode feed horn – i.e. the angular spread of the illumination in the far field (at the pupil of the input optics for instance) – is given by

θ ≈

2 ( f /# )

1 radians (13)

If we assume that the beam is circular in the far field then the solid angle subtended is given by:

Ω

= 2

(1 – cos(

)) (14)

≈

2

(1 – (1- 2

)) =

=

) /#

f ( 4

π

steradians (15)

The area of the beam at the focal plane waist is given by:

A = πw

=

λ²

)

/#

f (

4 mm

(16)

The throughput is therefore given by:

A

mm

sr (17)

and we have reproduced the well known result for diffraction limited throughput.

In principle measurement of the point spread function will give both the spatial extent of the intensity pattern at the focal plane – the equivalent waist radius, and, by Fourier transform, the angular spread of the beam in the far field. However, because we only measure the intensity it is not always possible to unambiguously disentangle the effects of any multi-mode response of the feedhorns and aberrations caused by misalignment or other systematic errors in the telescope simulator and/or instrument optics. It is highly desirable therefore to make a direct measurement of the angular extent of the beam directly at the instrument pupil image. This measurement also has the advantage of giving the beam filling factor compared to the full aperture of the telescope and is therefore a direct measurement of the point source coupling efficiency of the instrument.

One other science requirement that is verified during measurement of the point spread function is that

on the co-alignment of the arrays. The position of the image at the output focal plane of the telescope

simulator of a source placed at the input will be absolutely calibrated during the commissioning of the

telescope simulator. The beam conditioning optics of the source used at the input focal plane of the

telescope simulator will also be accurately calibrated. Therefore there will be absolute knowledge of the

position of the input source whatever its wavelength characteristics and both the alignment of the arrays

with respect to each other and their absolute alignment with respect to the telescope boresight can be

verified at FIR wavelengths.

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-8

Instrument Spatial Impulse Response

(SIRF - no units)

Relative response of a pixel as a function of near beam position in the focal plane of the telescope simulator. This defines the impulse response of the

instrument to a point source and is also used in determination of the instrument throughput.

The favoured method is to use an FIR laser focussed at the input focal plane of the telescope simulator. This gives a well defined illumination pattern on the telescope simulator pupil with a flat phase front. A blackbody source can also be used but this will be more difficult to interpret due to partial coherence and brightness problems. The image of the source is finely stepped over the position of the target pixel preferably in raster pattern to determine the 2-D impulse response.

In principle this measurement should be made for each pixel in each array. This may prove to take too long and a minimum sub-set of pixels for which this measurement will be carried out will be identified – see also optical distortion measurement below. It is also possible that shorter cross pattern is used for some pixels rather than the full raster. Both types of

measurement should be

available.

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-9

Telescope Pupil Illumination Function

(PIF – no units)

Relative response of a pixel as a function of position in the pupil plane of the telescope simulator.

This defines the illumination pattern of the instrument on the primary mirror of the Herschel telescope and is used for determination of the instrument throughput; the determination of the point source coupling efficiency and can be used to verify the measurement of the spatial impulse response.

A small source is scanned across the location of the image of the instrument cold stop. The method of realising this

measurement using the telescope simulator is described in RD2.

All pixels are measured with a single measurement – the preferred source to use here is the FIR laser however this restricts the measurement to a single channel per scan and the comparison between the laser and a black body should be done.

Although it is preferred that the full 2-D area of the pupil

response is explored this may be impossible due to practical difficulties with implementation.

At least a cross pattern

measurement should be possible.

3.1.4 SRD-R6/SRD-R8 Position of the Pixels on the Sky

The image of the detector arrays on the sky may not be perfect due to distortions introduced by the instrument optics. The arrays may also not be perfectly aligned with the telescope co-ordinate system.

The FIR images of the arrays on the sky can be determined by finding the centres of the response functions of pixels at strategic locations in the field of view. In principle this measurement is already covered by the measurement of the impulse response function of these pixels as described above.

However here the requirement on the knowledge of the input source characteristics are much less than required for the SIRF measurement because we are only interested in the centroids of the response functions. It will be sufficient to scan the image of a larger than point source black body across the output focal plane of the telescope simulator as long as the same source is used for each pixel position to be measured. Once the positions of the centroids of a subset of the pixels within an array have been determined, the positions of the others should be found from optical modelling and alignment

measurements on the arrays and the instrument optics.

If the output of the source is stable over time and repeated operations, then this measurement can also

be used to determine the relative efficiency of each of the pixels. This is useful in determining the

relative efficiency of the instrument as a function of position in the instrument field of view (see also

section on Relative Efficiency)

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-10

Pixel Relative Position Map ((

- arcsec)

Relative position of the centre of the response of each pixel in each array. The position is quoted in arcsec with respect to the boresight of the instrument.

This is used to reconstruct the pointing of each pixel on the sky for the construction of sky maps and the correct pointing of the telescope in flight.

A point like blackbody source is placed at the input focal plane of the telescope simulator and the image scanned is over the position of each pixel of interest.

In principle this measurement should be made for each pixel in each array. This may prove to take too long and a minimum sub-set of pixels for which this measurement will be carried out will be identified.

It is desirable that the source power be stable and repeatable – this will allow this

measurement to be used for

determination of the instrument

spatial relative response function

– see below.

3.1.5 SRD-R8/SRD-13/SRD-14 Crosstalk Map; Detector Frequency Response and Linearity

The detector frequency response and linearity should be characterised at unit level ahead of integration into the instrument. Indeed we will depend on this knowledge as all measurements on the PSF etc will likely need to be done with a chopped signal in order to overcome the large and potentially unstable background flux

. However, the frequency response will not have been verified with the flight like electronics and harnesses and a repeat of the unit level characterisation will be necessary on at least a few pixels. This forms part of the verification of the instrument relative response requirement being the relative frequency response of the instrument.

The method is straightforward: a black body is placed at the input to the telescope simulator and the image centred on the detector of choice – one of the overlapping detectors between the three arrays. A chopper is placed in front of the black body aperture and the signal recorded as the chop frequency is varied. The relative response of the detector versus frequency is thus established. From this it is a simple matter to determine the detector time constant. The responsivity in the frequency domain is given by:

R

(ν) = R

(1 + (2πν)

)

(18)

where

is given by

τdet

=

db

2

1

πν

seconds (19)

and

is the frequency at which the responsivity of the instrument falls to half of the DC responsivity R

.

While doing this test we can take advantage of the set up to test two other aspects of the instrument performance. Because we are recording data from all the pixels we will automatically have the dataset required to establish the degree of cross talk present between the detectors on an individual array. If we use instead a monochromatic source (an FIR laser) then we can also establish the degree of cross talk between different arrays. Again using a laser as a source would mean that this test could also be extended to test the linearity of the detector by inserting filters into the optical path of the laser we can attenuate it by an accurately known amount. Both the linearity and cross talk characteristics of the detection system can then be established over a wide range of signal power.

How many pixels will need to be tested in this way is not yet clear; it is probable that all of the pixels to be used for chopped observations will need to be fully characterised and, as time allows, a sub-set of the other detectors starting with the overlapping detectors across the arrays.

♣ Especially true because we have baselined a warm telescope simulator so the instrument will see a diluted room background

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-11

Cross Talk Map ( c

,c

- no units)

For each of i detectors, the relative response of the

detectors within the same array at position (x,y). An

array-to-array cross talk map might also be necessary so each pixel tested would then have three such matrices associated with it. Used for removing spurious signals from chopped observations and ghosting from mapping observations.

A point like blackbody or laser source is placed at the input focal plane of the telescope simulator and a chopper is placed in the optical beam. The data from all detectors is recorded and analysed for the presence of signals at the known frequency – these are compared to the signal recorded at the target detector to construct the relative response matrix.

In principle this measurement should be made for each pixel in each array. This may prove to take too long and a minimum sub-set of pixels for which this measurement will be carried out will be identified.

It is desirable that the source power be variable over a wide range in order to detect cross talk to a level <0.05%.

CRD-PAR-12

Detector Response Versus Input Power

(R

– no units)

For each detector this is the correction to be applied to the detected signal to refer it to the standard calibration signal. This correction removes any non- linear response of the detection system (detector plus

electronics) as a function of power at the input to the

instrument. The correction may be in the form of coefficients or a look up table. Several

corrections may be necessary as the non-linearity of the system could be a function of chop frequency and/or operating conditions.

A point like blackbody or laser source is placed at the input focal plane of the telescope simulator and a chopper is placed in the optical beam. The power in the beam can be varied using filters with predetermined attenuation. The same

measurement can be used with

the instrument in different

operating conditions and with

different chop frequencies to

complete the correction matrix.

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-13

Detector Time Constant (

– seconds)

For each detector this is the time constant used to correct the responsivity to the DC value for time varying signals of a known frequency. Its use is predicated on the assumption that the detection system behaves as a single pole RC filter. If this proves not to be the case then a single time constant per detector may not be enough to describe the frequency response of the instrument.

The time constant will depend on the operating conditions

(temperature; bias; background loading etc) of the detectors. It must be determined under a range of conditions to create a matrix that will allow us to predict what it will be during flight and to pick the optimum conditions for instrument operation.

A point like blackbody is placed at the input focal plane of the telescope simulator and a chopper is placed in the optical beam. The chopper frequency is varied from near DC to several times the known or estimated 3 dB frequency of the target detector with the signal recorded at each step in frequency. The same measurement can be used with the instrument in different operating conditions to determine the relationship between

operating condition and frequency response.

In principle this measurement

should be made for each pixel in

each array. This may prove to

take too long and a minimum

sub-set of pixels for which this

measurement will be carried out

will be identified.

3.1.6 SRD-R10/CRD-SR1 Spatial Relative Responsivity and Pixel NEP Map Once the absolute instrument DC responsivity has been established for a given set of operating conditions the responsivity of each pixel in each array can be determined relative to the nominal operating point. Variation in the instrument responsivity as a function of position might be due to a number of effects – detector responsivity; vignetting; change in the instrument bandpass as a function of position; change in the optical efficiency as a function of position etc. Whilst the measurement of the relative DC responsivity is established by the load curve measurement using a source that fills the field of view as described above, many of the other possible effects can only be tested using a correctly conditioned input beam. The measurement used for the determination of the pixel positions on the sky will also give a relative response versus position in the focal plane if the source used is sufficiently stable and repeatable.

To determine the NEP as a function of position in the focal plane we only need then to measure the noise under the same set of operating conditions as used for the determination of the DC responsivity.

The Pixel Nominal Load Noise Map (see above) will also be used to cross check the measured NEP.

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-14

Spatial Relative Responsivity (r

– no units)

Relative response of each pixel in each array with respect to a nominal pixel position and set of operating conditions. Whilst this may seem superfluous as we already have the absolute instrument responsivity as a function of position in the FOV, the determination of the absolute responsivity will be done, by necessity, using a source that fills the FOV uniformly. The spatial relative responsivity is the relative point source response of the instrument as a function of pixel position in the FOV. This is used to flat field the instrument image frames to allow

co-addition across different pixels.

A point like blackbody source is placed at the input focal plane of the telescope simulator and the image placed at the position of each pixel of interest and the signal recorded.

In principle this measurement should be made for each pixel in each array. This may prove to take too long and a minimum sub-set of pixels for which this measurement will be carried out will be identified.

The source power must be

stable and repeatable. This

measurement could be combined

with the measurement of the

pixel relative position map.

3.1.7 CRD-SR2/CRD-SR3/CRD-SR4 Relative Spectral Responsivity; Channel Central Wavelength and Bandpass; Out of Band Rejection

The spectral response of each of the instrument channels is the product of the spectral response of the detectors; the filter spectral transmission profile and the spectral transmission efficiency of the optics.

Whilst the first two of these can be, more or less, determined at unit level, the optics will not be verified in the FIR until the instrument is complete. Therefore, the combination, and any effects caused by such a combination, of all three must also be characterised at instrument level. The measurement of the spectral relative efficiency will be done by the use of an external spectrometer with a black body input source. The output of the spectrometer will be focussed at the input focal plane of the telescope simulator and the image placed at the position of each pixel to be measured in turn. At least a subset of pixels will be measured to the highest possible spectral resolution and good signal to noise to verify that there are no problems with channel fringing or other unaccounted for spectral features present. Other pixels may also be characterised at a lower resolution and/or with lower signal to noise as a confidence check.

Once the relative spectral response of the instrument, f

(

), has been determined the bandpass or equivalent width of each channel is given by:

∆λ = ^λ

∫

λ

λ λ

u

l

inst

( ) d

f (20)

And the central wavelength is given by

λc

=

∫

∫

λ λ λ

λ

λ λ

λ λ λ

u

l inst u

l inst

d ) ( f

d ) ( f

(21)

Here λl and λu are the lower and upper wavelength limits over which the external spectrometer operates. It is highly desirable that the spectrometer; telescope simulator and any filtering in the ground test system are able to operate at wavelengths well below and above the nominal bandpass of the instrument in order to verify the cleanliness of the instrument spectral bandpass. It is possible that the FIR laser could also be used to check the out of band rejection of the instrument in a semi-quantitative manner. Another method of checking the out of band rejection is to use a bright optical/NIR source with a suitable highpass (short wavelength) optical filter.

The resolution required for the test spectrometer should be such as to find any possible sources of

channel fringing within the instrument. We do not expect efficient interference to occur in the

instrument at equivalent resolving powers greater than a few hundred and the narrowest features

present in the filters will be at much lower resolution than this. Therefore an external spectrometer with

a resolution of several hundred at the longest wavelength of interest should be sufficient.

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-15

Spectral Relative Responsivity (f

(λ) – no units)

Relative response of each pixel in each array as a function of wavelength. This is used to colour correct the measured fluxes of objects with known or assumed continuum spectra. It is also used to determine the equivalent width and central wavelength of each channel. In the spectrometer channels the spectral relative responsivity is used to spectrally “flat field” the measured source spectra. It is especially important that this parameter is accurately determined for each

spectrometer pixel as all are used for taking astronomical spectra.

A test spectrometer is used to feed the input focal plane of the telescope simulator. The output of the spectrometer should be as near to a point source as

possible. The image of the test spectrometer output is placed at the position of a pixel and the wavelength (or position if an FTS) scanned. This

measurement should be done at high (R~few hundred-thousand) resolution and with good s/n (~1000 per spectral bin) in order to accurately determine the relative spectral response function of the instrument. Each pixel in the spectrometer channel must be measured to high

accuracy; only the overlap pixels in the photometer arrays need be measured with high accuracy.

Other pixels maybe measured at

low resolution if time allows.

3.1.8 SRD-R13 Temporal Relative Responsivity

The final aspect of the relative responsivity requirement that requires verification is the requirement to be able to make repeated observations of the same source and achieve the same answer in terms of the flux measured. In order to achieve this the detection system must be intrinsically temporally stable and we must have a method of determining its stability both on ground and in flight. One method of doing this is to measure the signal from a known and stable source with the instrument in a known operating condition at intervals that sample a wide frequency range. This will show whether there are changes in the instrument responsivity over time and their characteristic frequencies. On the ground this might be achieved by placing the instrument into a given stable operating condition – photometer scan mode say – and using a stable external source (it doesn’t need to be of known output, just very stable and

repeatable) to make measurements of the instrument relative response at intervals of a few minutes up to, say, 24 hours. This measurement will be a verification of the intrinsic stability rather than a

calibration and no calibration parameter is derived.

In flight this is more difficult as it may not always be possible to acquire a calibration target at convenient times. Therefore, we have incorporated a calibration source into the design of the

instrument that will illuminate all pixels in both the spectrometer and photometer channels. We require that this calibration source be characterised during ground testing so that its performance can be verified and its output calibrated against a known external reference source. This can be done by operating the calibrator during the calibration of the DC responsivity of the instrument to give a small amount of extra input power onto the detectors. The delta signal seen on top of the known load gives a correlation between equivalent power seen at the entrance to the instrument and the set point for the calibrator.

The response at each detector may be different, as the calibrator may not be seen equally well by all

detectors in all arrays. The stability of the calibrator output is therefore important and this must be

tested at the same time as the detection system stability.

Parameter/notation/units Description and use Outline Ground

Measurement Method CRD-PAR-16

Calibrator Equivalent Power (CR – W per step)

Calibration between the

operating set point of the internal calibrator and the signal seen on the detectors under nominal operating conditions. This can be converted to an equivalent flux referred to the input aperture of the instrument.

The calibrator is used for testing the stability of the detection system and this calibration will be used to determine the optimum operation of the

calibrator in flight. Several types of calibration may be necessary to give maximum flexibility to the method of in flight calibration.

In order to absolutely calibrate the equivalent flux from a small step in the calibrator output a blackbody can be placed in the beam of the instrument and set to give the same flux as used for the DC responsivity calibration.

The instrument is set to its nominal operating condition (bais; temperature etc) and the calibrator cycled between on and off with a small output step To provide a stable output the calibrator may have to be driven at the upper end of its

temperature range, therefore this step may be done on top of a DC pedestal. The net DC signal will be arranged to be the same by reducing the load from the external blackbody.

This can be repeated for different flux levels and

calibrator and detector operating

conditions.

3.1.9 SRD-R12 Photometer Absolute Radiometric Accuracy

The ultimate photometric accuracy in the photometer channels depends on all the parameters discussed above and the errors generated in their measurement. The statistical errors can be minimised using long integration times during ground testing and systematic errors minimised by design. However, systematic errors cannot be fully eliminated and we should not suppose that the ground test has generated an unambiguous absolute calibration of the instrument. Additionally, some aspects of the Herschel system level performance (pointing accuracy and reconstruction; telescope effective area etc) will effect the achievable absolute photometric accuracy and these will not be known or fully tested until Herschel is in orbit. Therefore, while there will be a verification of the potential for absolute photometry with SPIRE during ground testing, the ultimate test will be done in flight using a number of calibration targets with known spectral characteristics (see later).

The one aspect of instrument level performance that may place a fundamental limit on the photometric accuracy is the stability and repeatability of the instrument responsivity. This in turn is a complex function of the temperature stability of the various stages and the electronics performance. At

instrument level we can characterise the impact of temperature drifts in the FPU and the electronics but

we will only be able to qualitatively assess the absolute system stability. See also the discussion on the

calibrator stability; this too is important as it will be used to monitor and correct any drifts in internal

responsivity.